How do I make a reference image in Blender show up when rendering the scene?
The whole point of reference images are to help while modeling and setting up a scene, they are not intended to be in the final rendered image.

Blender includes an addon called import images as planes, enable this addon and you get an extra import option File->Import->Images as Planes. Using this will setup your image as a texture on a plane so that it will show up in the final render.